
theorem
  for G1 being edgeless _Graph, G2 being _Graph
  holds G1 is Subgraph of G2 iff the_Vertices_of G1 c= the_Vertices_of G2
proof
  let G1 be edgeless _Graph, G2 be _Graph;
  thus G1 is Subgraph of G2 implies the_Vertices_of G1 c= the_Vertices_of G2
    by GLIB_000:def 32;
  assume A1: the_Vertices_of G1 c= the_Vertices_of G2;
  for e being set st e in the_Edges_of G1 holds
    (the_Source_of G1).e = (the_Source_of G2).e &
    (the_Target_of G1).e = (the_Target_of G2).e;
  hence thesis by A1, XBOOLE_1:2, GLIB_000:def 32;
end;
